Analysis of Sparse Quasi-Newton Updates with Positive Definite Matrix Completion

作     者：Yu-Hong Dai Nobuo Yamashita 

作者机构：State Key Laboratory of Scientific and Engineering ComputingInstitute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesP.O.Box 2719Beijing 100080People’s Republic of China Department of Applied Mathematics and PhysicsGraduate School of InformaticsKyoto UniversityKyoto 606-8501Japan 

出 版 物：《Journal of the Operations Research Society of China》 (中国运筹学会会刊（英文）)

年 卷 期：2014年第2卷第1期

页      面：39-56页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work was supported by the Chinese NSF Grants(Nos.11331012 and 81173633) the China National Funds for Distinguished Young Scientists(No.11125107) the CAS Program for Cross&Coorperative Team of the Science&Technology Innovation The authors are grateful to Professors Masao Fukushima and Ya-xiang Yuan for their warm encouragement and valuable suggestions.They also thank the two anonymous referees very much for their useful comments on an early version of this paper 

主　　题：Quasi-Newton method Large-scale problems Sparsity Positive definite matrix completion Superlinear convergence 

摘      要：Based on the idea of maximum determinant positive definite matrix completion,Yamashita(Math Prog 115(1):1–30,2008)proposed a new sparse quasi-Newton update,called MCQN,for unconstrained optimization problems with sparse Hessian *** exchange of the relaxation of the secant equation,the MCQN update avoids solving difficult subproblems and overcomes the ill-conditioning of approximate Hessian ***,local and superlinear convergence results were only established for the MCQN update with the DFP *** this paper,we extend the convergence result to the MCQN update with the whole Broyden’s convex *** results are also reported,which suggest some efficient ways of choosing the parameter in the MCQN update the Broyden’s family.